Lattice Dynamics and Electron Pairing in High Temperature Superconductors -- Direct Arpes and TC Enhancement in Compressively Strained LSCO-214 Films -- Full Fermi Surface of a High Temperature Superconductor Revealed by Angular Magnetoresistance Oscillations -- Sum Rules and Energy Scales in BiSrCaCuO -- Optical Properties of (Pr,Ce)2CuO4 -- Tunneling Spectra Near Tc Inoverdoped Bi2Sr2CaCu2O8+? -- Andreev — Saint James Reflections as a Tool for the Study of Unconventional Superconductors -- Bi2Sr2CaCu2O8+? C-Axis Bicrystal Twist and Cross-Whisker Experiments -- Nodeless Pairing State in Yba2Cu3O7 -- Nuclear Spin Relaxation and Incommensurate Magnetism in Doped Cuprates -- Antiferromagnetic Vortex Core in Htsc Studied by Spatially-Resolved NMR -- Exploring the Oxygen Order in Hg -1223 and Hg -1201 by 199Hg Mas Nmr -- Two Fluids Formation in the Normal State of High-TC Superconductor -- Temperature Dependence of In-Plane Resistivity of Ybco -- Measurements of the Doping Effects on the In-Plane Paraconductivity in Cuprate Superconductors -- A Possibility of a Phase Fluctuationlike Effect in Htsc Cuprates -- Pseudogap Behavior in Underdoped Cuprates -- Notes on Rvb-Vanilla by Anderson et al. -- Enhanced Tc Near the Metal/Insulator Transition: A New Perspective on Unconventional Superconducting Materials -- Electron-Lattice Interaction in Htsc Curates -- High-Temperature Superconductivity of Oxides -- Bose-Einstein Condensation in a Bosonfermion Model of Cuprates -- Oxygen-Related Band-Features of the Extended Emerymodel for the Hts Cuprates -- Condensation Energy for Spin Fluctuations Mechanism of Pairing in High-Tc Superconductors -- Effects of Disorder with Finite Range on the Properties of D-Wave Superconductors -- Superconductivity in the Background of Two-Dimensional Stripe Superstructure -- Theory for Key Experiments in Cuprate Superconductors -- Dynamical Spin Susceptibility in Singlet-Correlated Band Model -- Stripe-Like Inhomogeneities, Coherence, and the Physics of the High tc Cuprates -- Self-Supported Superconductivity in Layered Metalochloronitrides -- First Order Superconducting Transition Near a Ferromagnetic Quantum Critical Point -- Structures and Superconducting Properties of Sodium Cobalt Oxides -- Upper Critical Field for Cobalt Oxide Superconductors -- Disproportionation and Spin Ordering Tendencies in NaxCoO2 AT x = 1/3 -- Interband Scattering in MgB2 -- Phonon Structure in Point-Contact Spectra of MGB2 -- A Theoretical Approach to Design Unconventional Superconductors by Heterocyclic Molecules.This volume contains the proceedings of the 2004 University of Miami Workshop on Unconventional Superconductivity. The workshop was the fourth in a series of successful meetings on High-T Superconductivity and C related topics, which took place at the James L. Knight Physics Building on the University of Miami campus in Coral Gables, Florida, in January 1991, 1995, 1999, and 2004. The workshop consisted of two consecutive events: 1. NATO Advanced Research Workshop (ARW) on New Challenges in Superconductivity: Experimental Advances and Emerging Theories, held on January 11-14, 2004; 2. Symposium on Emerging Mechanisms for High Temperature Superconductivity (SEMHTS), held on January 15-16, 2004. It is hard to write a balanced preface to a volume like this one, yet at least we try to offer the reader a taste of what was happening in this workshop. There were close to a hundred scientists from around the world, albeit fewer Russians than we had originally hoped for. Nevertheless, the workshop was very lively and we trust that this is demonstrated in this volume. The workshop included high-quality presentations on state of the art works, yet a key issue, discussed by many, was how homogeneous the cuprates are. STM data, as well as other reports, showed that the cuprate superconductors (SC’s) studied were inhomogeneous, especially in the underdoped regime; while experiments, like ARPES and magnetoresistance have established the existence of a Fermi Surface (FS), at least above some doping level, in the cuprates.